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16 [26] THEAETETUS EUDOXUS [27] than sounds of low pitch, which was wrong. He is also supposed to have invented the pulley. [26] THEAETETUS (thee'uh-tee'tus) Greek mathematician
B.C.
Died: Athens, 369 b . c . Theaetetus was the son of a rich Athe nian whose money was apparently squandered by those in charge of it be fore it could reach the young heir. De spite that, he had apparently the advan tage of the kind of education and up bringing that wealth could bring, study ing at Plato’s Academy. Plato [24] thought enough of him, apparently, to make him a character in two of his dialogues, one of them called “Theae tetus.” He died in action in battle against the city of Corinth in one of the endless stupid wars the Greek cities fought against each other in those days. The Pythagoreans had discovered the irrationality of the square root of two. Theaetetus apparently systematized the study of these irrationals to show that there were large numbers of them and, apparently, an infinite number. That rather drew the fangs of their mystery. One is an anomaly; many are normal. He studied the five regular solids of Plato and may have been the first to demonstrate that there were, in fact, only those five and that no other regular polygons could exist. [27] EUDOXUS (yoo-dok'sus) Greek astronomer and mathe matician
Bom: Cnidus (on what is now the Turkish coast), about 400 b .
. Died: Cnidus, about 347 B.C.
Eudoxus studied under Archytas [25] and also at Plato’s [24] Academy under difficult circumstances. Being poor, he lived in Piraeus, Athens’ port city, where quarters could be obtained more cheaply. This meant he had to walk five miles to school every morning and five miles back every evening. After graduating, he traveled to Egypt for what we would today call post graduate work in astronomy. Thereafter he established a school of his own in Cyzicus on the northwestern coast of what is now Turkey. Eventually he transferred it to Athens, where he taught for many years. As a now successful and established philosopher, he visited his old teacher Plato again and was rewarded with a banquet in his honor. (He may even have served as active head of the Academy while Plato was in Sicily in 367
b . c .) During those years he introduced many geometric proofs that later found their way into the summarizing work of Euclid [40]. He also began to work with systematic approximations of lengths and areas that could not be determined directly, something developed further a century later by Archimedes [47]. Eudoxus accepted Plato’s notion that the planets moved in perfect circles as a matter of necessity, but, having observed the motions of the planets, he could not help but realize that the actual planetary motions were not those of objects mov ing evenly in perfect circles. He was the first to try to adjust Plato’s theory to actual observation to “save the appearances” as it was called. He suggested that the sphere into which a planet was set had its poles set into an other sphere which had its poles set into still another sphere and so on. Each sphere rotated evenly, but the combina tion of speeds and the inclination of the poles of one sphere to those of the next resulted in the overall motion of the planet being the irregular one that was actually observed. Thus, by combining perfect regularities, the observed imper fection of irregularity was achieved. The appearances were saved, and so was Plato. Eudoxus also drew a new map of the earth, better than that of Hecataeus [9] and was the first Greek to attempt a map of the stars. He divided the sky, for this purpose, into degrees of latitude and lon gitude, a notion eventually transferred to the surface of the earth itself. In later 17 [28] HERACLEIDES ARISTOTLE [29] centuries, Cicero considered Eudoxus the greatest of the Greek astronomers, though this may be unjust to Hipparchus [50], Unfortunately, none of the writings of Eudoxus survive. [28] HERACLEIDES (her-uh-kly'deez) Greek astronomer
Bander Eregli, on Black Sea shore about 150 miles east of Istanbul, Turkey), about 388 b .
. Died: Athens, 315 b . c . Heracleides (often called Heracleides Ponticus after his birthplace) traveled to Athens as a young man, for it was then the center of the philosophic universe, and studied in Plato’s Academy. He must have done well, for there is a story that when Plato [24] went to Sicily in his ill-fated venture to make a king a philos opher, Heracleides was left in charge of the school (other stories say Eudoxus [27] was). Heracleides wrote a good deal on as tronomy and geometry, but little of his work survives. He is known today only for certain suggestions in astronomy that were very important, although they re mained uninfluential in his own time. The heavenly objects generally, and in particular the fixed stars, take part in an even rotation about the earth from east to west. It had always been assumed that this apparent rotation was a real one, that the vault of heaven actually turned. Heracleides pointed out that the same effect would be observed if the heavens stood still and if the earth rotated about its axis from west to east once every day. Heracleides was the first man we know of to suggest the rotation of the earth, but the idea was not to become domi nant in the world of astronomy until the time of Copernicus [127], eighteen hun dred years later. Against the background of the stars (considered as unmoving points), the sun, moon, and five known planets— Mercury, Venus, Mars, Jupiter, Saturn— moved from west to east in rather erratic fashion. It was this erratic west-to-east motion superimposed on the motion of the starry vault that Eudoxus had tried to explain by assigning each body a number of separate spheres. Of these various bodies, the motions of two, Mercury and Venus, were pecu liar in that they were never very far from the position of the sun. The spheres of Eudoxus could explain this, at least approximately, but it seemed to Hera cleides that a more straightforward ex planation was the supposition that Mer cury and Venus revolved about the sun and therefore could not depart very far from that body. Heracleides kept the earth in the cen ter of the universe but was nevertheless the first to suggest the revolution of one heavenly body about another. He differed from Philolaus [19] in suggesting a revolution about a visible and actual body, the sun, and not about a mystical and unseen one such as the “central fire.”
This beginning of a heliocentric theory was carried further by Aristarchus [41] a century later but lost out to the contrary views of Hipparchus [50]. This portion of Heracleides’ concept had also to await Copernicus for vindication. [29] ARISTOTLE (ar'is-totl) Greek philosopher Born: Stagira (in northern Greece), 384 b .
. Died: Chalcis (on the Aegean is land of Euboea, now Evvoia), 322 b
c . Inland from Stagira was the semi Greek kingdom of Macedon, with which Aristotle’s family was closely connected. Aristotle’s father, for instance, had been court physician to the Macedonian king, Amyntas II. Aristotle lost both parents while a child and was brought up by a friend of the family. He is supposed to have spoken with a lisp and to have been something of a dandy. At the age of seventeen Aristotle trav eled to Athens for a college education and after Plato [24] returned from Syra cuse, the young man joined Plato’s Academy, where he studied assiduously. 18 [29] ARISTOTLE ARISTOTLE [29] Eventually he was to become by far the most renowned of all the pupils of Plato. Plato called him “the intelligence of the school.” When Plato died in 347 b .
., Aristotle left the school. The reason he gave was that he disapproved of the growing em phasis on mathematics and theory in the Academy and the continuing decline in natural philosophy. However, it is possi ble that he may have been displeased that Plato, on his deathbed, designated his nephew, an undistinguished person, as his successor, passing over the merits of Aristotle. It is also true that Athens and Macedon were enemies at the time and Aristotle may have felt uneasily con scious of being considered pro-Mac edonian.
In any case Aristotle found it expedi ent to set out upon a journey that car ried him to various parts of the Greek world, particularly to Asia Minor. While there he married and engaged in the study of biology and natural history, al ways his chief love. In 342
b . c . he was called to Macedon. The son of Amyntas II had succeeded to the throne of Macedon as Philip II while Aristotle was at the Academy, and now the king wanted the son of his father’s physician back at court. The purpose was to install him as tutor for his four teen-year-old son, Alexander. Aristotle held this position for several years. Since Alexander was to become Alexander the Great, the conqueror of Persia, we have the spectacle of the greatest soldier of ancient times being tutored by the greatest thinker. In 336
b . c . Philip II was assassinated and his son succeeded as Alexander III. Alexander had no further time for edu cation so Aristotle left Macedon the next year and went back to Athens, while Alexander went on to invade the Persian Empire in a great conquering campaign. Aristotle’s nephew, Callisthenes, accom panied Alexander, but Aristotle’s in fluence over his erstwhile pupil was not very great for in 327 b .
. Callisthenes was executed by the increasingly megalo maniac monarch. Meanwhile, in Athens, Aristotle founded a school of his own, the Ly ceum, so called because Aristotle lec tured in a hall near the temple to Apollo Lykaios (Apollo, the Wolf-God). It was also called the “peripatetic school” (“walk about”) because Aristotle, at least on occasion, lectured to students while walking in the school’s garden. He also built up a collection of manuscripts, a very early example of a “university li brary.” It was this which eventually served as the kernel for the great Library at Alexandria. The school continued under Aristotle’s directorship quite successfully, empha sizing natural philosophy. In 323 b . c .,
however, the news arrived of the death of Alexander the Great in Babylon. Since Aristotle was well known to have been Alexander’s tutor, he feared that an anti-Macedonian reaction in Athens might lead to trouble. And, indeed, the accusation of “impiety” was raised. Aris totle had no mind to suffer the fate of Socrates [21]. Saying he would not allow Athens to “sin twice against philos ophy” he prudently retired to Chalcis, his mother’s hometown, and died there the next year. Aristotle’s lectures were collected into nearly a hundred and fifty volumes and represent almost a one-man encyclopedia of the knowledge of the times, much of it representing the original thought and observation of Aristotle himself. Nor was it confined entirely to science, for Aris totle dealt with politics, literary criticism, and ethics. Altogether, of the volumes attributed to him, some fifty have sur vived (not all of which are certainly au thentic), a survival record second only to that of Plato. This survival came about through a fortunate chance. Many of his manu scripts were found in a pit in Asia Minor about 80 b .
. by men in the army of the Roman general Sulla. They were then taken to Rome and recopied. The one field for which Aristotle is not noted is mathematics, but even here he may be credited with a glancing blow, for he is the virtual founder of the sys tematic study of logic, which is allied to mathematics. He developed, in great and satisfying detail, the art of reasoning from statement to necessary conclusion 19 [29] ARISTOTLE ARISTOTLE [29] and thereby demonstrating the validity of a line of thought. His system stood without major change until the nine teenth-century development of symbolic logic by Boole [595], which converted logic into a branch of mathematics in form as well as spirit Aristotle’s most successful scientific writings were those on biology. He was a careful and meticulous observer who was fascinated by the task of classifying ani mal species and arranging them into hierarchies. He dealt with over five hun dred animal species in this way and dis sected nearly fifty of them. His mode of classification was reasonable and, in some cases, strikingly modern. He was particularly interested in sea life and ob served that the dolphin brought forth its young alive and nourished the fetus by means of a special organ called a pla centa. No fish did this, but all mammals did, so Aristotle classed the dolphin with the beasts of the field rather than with the fish of the sea. His successors did not follow his lead, however, and it took two thousand years for biologists to catch up to Aristotle in this respect. It was J. Müller [522] who finally confirmed Aris totle in this respect. Aristotle also stud ied viviparous sharks, those that bear live young—but without a mammalian pla centa.
He also noted the odd ability of the torpedo fish to stun its prey though, of course, he knew nothing of the electric shock with which it managed it. He was also wrong on occasion, as when he de nied sexuality in plants. Nineteen cen turies were to pass before Alpini [160] was to correct this particular error. His formation of a hierarchy of living things led him irresistibly toward the idea that animals represented a chain of progressive change, a sort of evolution. Other Greek philosophers groped simi larly in this direction. However, barring any knowledge as to the physical mecha nism whereby evolutionary changes could be brought about, such theories in variably became mystical. A rational theory of evolution had to await Darwin [554], twenty-two hundred years after the time of Aristotle. Aristotle studied the developing em bryo of the chick and the complex stom ach of cattle. He decided that no animal had both tusks and horns, and that no single-hooved animal had horns. But his intuition sometimes led him astray. He believed the heart was the center of life and considered the brain merely a cool ing organ for the blood. In physics Aristotle was far less suc cessful than in biology, perhaps because he was too Platonic. He accepted the heavenly spheres of Eudoxus [27] and Callippus [32] and even added further to them, reaching a total of 54. He seemed to think of the spheres as having an ac tual physical existence whereas Eudoxus probably thought of them as imaginary aids to calculation, as we consider the lines of latitude and longitude we draw on a map. Aristotle also accepted the four elements of Empedocles [17] but re stricted them to the earth itself. He suggested a fifth element, “aether,” of which all the heavens were composed. (We still use phrases such as “ethereal heights” today.) This fine of reasoning led him to agree with the Pythagoreans that earth and heaven were subjected to two different sets of natural law. On the earth all things were changeable and corrupt, while in the heavens all was permanent and unchanging. On earth the four ele ments each had its own place, and mo tion was an attempt to reach that place. Earth was in the center, water above it, air above that, and fire highest of all the earthly substances. Therefore an object composed largely of earth, such as a rock, would, if suspended in air, fall downward, while bubbles of air trapped underwater would move upward. Again, rain fell, but fire rose. It also seemed to Aristotle that the heavier an object was, the more eagerly it would strive to achieve its proper place, since the heaviness was the mani festation of its eagerness to return. Hence a heavier object would fall more rapidly than a lighter one. (Nineteen centuries later, a reconsideration of this problem by Galileo [166] was to lead to momentous consequences.) The motion of heavenly objects, on the other hand, was no attempt to get 2 0
[29] ARISTOTLE THEOPHRASTUS [31] anywhere. It was a steady, permanent motion, even and circular. Aristotle, apparently, was not an ex perimentalist for all that he was a close observer. He observed that rocks fell more quickly than feathers, but he made no attempt to arrange an observation of the falling of rocks of graded weight. Furthermore, neither he nor any other ancient scholar properly appreciated the importance of precise, quantitative mea surement. This was not mere perversity on their part, for the state of instru mentation was rudimentary indeed in an cient times and there were few clear methods of making accurate measure ments. In particular, they could not mea sure small intervals of time accurately, a deficiency that was to remain for two thousand years until the time of Huygens [215].
Aristotle rejected Democritus’ atom ism, dooming that concept through an cient and medieval times. On the other hand, he accepted the Pythagorean no tion of the roundness of the earth, pre senting his reasoning in a fashion that remains valid today. The most telling ar gument was that as one travels north, new stars appear at the northern horizon while old ones disappear at the southern. If the earth were flat, all stars would be equally visible from all points on its sur face. It was Aristotle’s championing of this view that kept it alive through the darkest days that were to follow. Upon Aristotle’s retirement, leadership of the Lyceum fell to his friend and pupil Theophrastus [31] and after him to Strato [38], under whom the Lyceum continued to be a vital and progressive force. Aristotle’s system of philosophy was never as influential in ancient times as Plato’s. Indeed, Aristotle’s works may not have been published for some cen turies after his death. After the fall of Rome, his work was largely lost to Europe (only Organon, his work on logic, was saved) while Plato’s works were, for the most part, retained. How ever, Aristotle’s books survived among the Arabs, who valued them highly. Christian Europe regained Aristotle from the Arabs, translating his books into Latin in the twelfth and thirteenth centuries. From that time Aristotle re placed Plato as the Philosopher. His views came to be regarded as possessing an almost divine authority, so that if Aristotle said it was so, it was so. By a queer fatality, it almost seemed as though his statements were most ac cepted when they were most incorrect. This cannot be blamed on Aristotle, who was himself no believer in blind obedience to authority. Nevertheless, fol lowing the era of over-adulation, he be came the very symbol of wrongness, and when the Scientific Revolution took place in the sixteenth and seventeenth centuries, its first victories involved the overthrow of Aristotelian physics. In the centuries since, Aristotle has, as a conse quence, too often been viewed as an enemy of science, whereas actually he was one of the truly great scientists of all time and even his wrongness was ratio nal. No man should be blamed for the stubborn orthodoxy of those who many centuries later insist they speak in his name. [30] MENAECHMUS (mih-nek'mus) Greek mathematician Born: about 380 b . c .
Nothing is known of Menaechmus’ life except that he may have been a stu dent of Eudoxus [27]. He seems to have been the first to take up the geometry of the cone system atically and to show that ellipses, parab olas and hyperbolas are all curves pro duced by the intersection of a cone and a plane. This work was continued by Archimedes [47] and Apollonius [49] and was to be given startling and pro found application to the real universe by Newton [231]. [31] THEOPHRASTUS (thee-oh-fras'- tus) Greek botanist Born: Eresus, Lesbos (an Aegean island), about 372 b .
. Died: Athens, about 287 b . c .
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